We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+3
60
1
avatar+212 

The lengths of four sides of a trapezoid have the ratios 1: 1: 1: 2. The area is equal to 48√3. What is the perimeter of the figure? I divided the figure into two 30-60-90 triangles and a quadrilateral. Are there any isosceles trapezoid properties I need to use. Please try to find the solution.

 Nov 2, 2019
 #1
avatar+105238 
+4

We can imagine an isosceles trapezoid  with equal sides  = S, a top base of S, and a bottom base of 2S

 

The height of the trapezoid can be found as :

 

√[ S^2 - [(1/2)S]^2 ]  =  √[(3/4)S^2]=   √3 S / 2

 

So.....the area  =   (1/2)Height * (Sum of the bases).....so we have that

 

48√3  = (1/2) ( √3 S)/2 * (S + 2S)

 

48√3  = (√3S / 4) * (3S)

 

48  =  S / 4 * (3S)

 

192 =  3S^2       divide both sides by 3

 

64  = S^2          take the positive root

 

8  = S

 

So the perimeter is  S + S+ S + 2S  =    3S + 2S   =   5S  = 5 (8)   =  40 units

 

 

cool cool cool

 Nov 2, 2019

11 Online Users

avatar
avatar